MECH325 - Homework Hints, Answers, and Extra Requirements

Homework 3 (Chapter 4b)

TO ENHANCE YOUR LEARNING, PLEASE TRY TO WORK THE PROBLEMS FIRST WITHOUT LOOKING AT THE HINTS AND ANSWERS BELOW.

MAKE SURE YOU SATISFY ALL REQUIREMENTS LISTED BELOW AND IN THE ORIGINAL PROBLEM STATEMENTS (UNLESS INDICATED OTHERWISE BELOW).

NOTE - BECAUSE MOST ANSWERS ARE PROVIDED, IT IS VERY IMPORTANT THAT YOU SHOW ALL STEPS IN YOUR WORK.  THE GRADING WILL BE BASED ON THE COMPLETENESS, CLARITY, AND CORRECTNESS OF YOUR WORK, NOT JUST THE ANSWERS YOU PROVIDE.

4.38
[30 pts]
  • For parts (a) and (b) consider stresses only at the top, bottom, and side points on the surface of the part at the fixed mount end (i.e., don't consider stresses at the "elbow" in the middle of the crank).
  • account for bending, torsion, and transverse shear
  • report the maximum shear stress and maximum principal stress for the largest Mohr Circle for parts (a) and (b)
  • (a) τmax = 95.0 MPa, σ1 = 144 MPa
  • (b) τmax = 84.2 MPa, σ1 = 84.2 MPa
4.43
[30 pts]
  • calculate F from a torque balance equation
  • draw shear and bending moment diagrams in two planes
  • use an x axis along the shaft (from bearing A to bearing B) and a vertical y axis, so plot diagrams in the xy plane (front view) and the xz plane (bottom view)
  • MA = MB = 0
  • Find the point where the resultant moment [Mr = sqrt (Mxy2  + Mxz2 )] is maximum. You might find Example 2.33 (2.20) helpful in trying to understand this part. Be careful to not combine moment components from different points along the shaft.
  • ignore all transverse shear effects
  • the stress components at the most severe state of stress are: Σ = 57.4 MPa; τ = 18.9 MPa
  • Σ1 = 63 MPa; τmax = 34.3 MPa
4.55
[15 pts]
  • τmax = 225 MPa
4.59
[25 pts]
  • draw shear and bending moment diagrams
  • Kt = 1.65 [Note - when values or answers like these are provided, you still need to show the work of how you arrive at them. This is the case with all problems in all assignments.]
  • σ1 = 12.4 MPa